INSTITUTE OF PHYSICS PUBLISHING JOURNAL OF PHYSICS: CONDENSED MATTER J. Phys.: Condens. Matter 13 (2001) L495–L502 www.iop.org/Journals/cm PII: S0953-8984(01)22448-5 LETTER TO THE EDITOR A Hartree–Fock study of charge redistribution in a two-dimensional mesoscopic structure A Kambili 1 , H Fehrmann 2 , C J Lambert 2 and J H Jefferson 3 1 Department of Physics, University of Bath, Claverton Down, Bath BA2 7AY, UK 2 School of Physics and Chemistry, Lancaster University, Lancaster LA1 4YB, UK 3 Defence Evaluation and Research Agency, St Andrews Road, Malvern, Worcs WR14 3PS, UK E-mail: pysak@bath.ac.uk (A Kambili) Received 2 March 2001 Abstract In this letter, we investigate the ground state of two-dimensional disordered cylinders which contain spinless, interacting electrons using the Hartree– Fock approximation. Calculations of the deviation of the polarization from uniformity reveal a tendency of the charge to rearrange towards the ends of the system. The presence of disorder results in fluctuations of the deviation around its mean value, which are more pronounced when the disorder strength is of the order of the interaction between the electrons. The existence of persistent currents in normal mesoscopic rings threaded by a magnetic flux [1] has stimulated a great deal of experimental and theoretical work [2–13]. More recently, there have been studies of the ground state of one-dimensional rings containing spinless fermions [14–16] which take into account both electron–electron interactions and disorder. Strongly disordered rings with short-range interactions and a half-filled band exhibit a reorganization of the charge in the ground state. The charge density changes from an inhomogeneous configuration due to the presence of the strong disorder to a periodic array of charges as a result of the interactions. In the present letter, we study the ground state of two-dimensional cylinders which contain spinless, interacting electrons via Coulomb interactions, by solving self-consistently the Hartree–Fock equation. The validity of the method has already been established [17] by studying the ground state of one-dimensional disordered rings and finding good agreement with the exact calculations [16]. Our aim is to examine reorganization of the charge in the ground state and, in particular, the manner in which charge tends to polarize towards the ends of the cylinder, thereby producing spontaneous dipole or quadrupole moments. The system under investigation is a two-dimensional cylinder, formed by a tight-binding lattice with M sites in the longitudinal direction (x ) and L sites in the transverse direction (y ). We take periodic boundary conditions along the longitudinal direction and free boundary 0953-8984/01/220495+08$30.00 © 2001 IOP Publishing Ltd Printed in the UK L495